Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

ATP and Presentation Service for Mizar Formalizations

This paper describes the Automated Reasoning for Mizar (MizAR) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP assistance to Mizar authors in finding and explaining proofs, and offers generation of Mizar problems as challenges to ATP systems. The service is based on a sound translation from the Mizar language to that of first-order ATP systems, and relies on the recent progress in application of ATP systems in large theories containing tens of thousands of available facts. We present the main features of MizAR services, followed by an account of initial experiments in finding proofs with the ATP assistance. Our initial experience indicates that the tool offers substantial help in exploring the Mizar library and in preparing new Mizar articles

Specifying Reusable Components

Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal verification of reusable components. Model-based contracts conservatively extend the classic Design by Contract with a notion of model, which underpins the precise definitions of such concepts as abstract equivalence and specification completeness. Experiments applying model-based contracts to libraries of data structures suggest that the method enables accurate specification of practical software

Unifying Requirements and Code: an Example

Requirements and code, in conventional software engineering wisdom, belong to entirely different worlds. Is it possible to unify these two worlds? A unified framework could help make software easier to change and reuse. To explore the feasibility of such an approach, the case study reported here takes a classic example from the requirements engineering literature and describes it using a programming language framework to express both domain and machine properties. The paper describes the solution, discusses its benefits and limitations, and assesses its scalability.Comment: 13 pages; 7 figures; to appear in Ershov Informatics Conference, PSI, Kazan, Russia (LNCS), 201

Using CamiTK for rapid prototyping of interactive Computer Assisted Medical Intervention applications

Computer Assisted Medical Intervention (CAMI hereafter) is a complex multi-disciplinary field. CAMI research requires the collaboration of experts in several fields as diverse as medicine, computer science, mathematics, instrumentation, signal processing, mechanics, modeling, automatics, optics, etc

Agent-based simulation of open source evolution

We present an agent-based simulation model developed to study how size, complexity and effort relate to each other in the development of open source software (OSS). In the model, many developer agents generate, extend, and re-factor code modules independently and in parallel. This accords with empirical observations of OSS development. To our knowledge, this is the first model of OSS evolution that includes the complexity of software modules as a limiting factor in productivity, the fitness of the software to its requirements, and the motivation of developers. Validation of the model was done by comparing the simulated results against four measures of software evolution (system size, proportion of highly complex modules, level of complexity control work, and distribution of changes) for four large OSS systems. The simulated results resembled the observed data, except for system size: three of the OSS systems showed alternating patterns of super-linear and sub-linear growth, while the simulations produced only super-linear growth. However, the fidelity of the model for the other measures suggests that developer motivation and the limiting effect of complexity on productivity have a significant effect on the development of OSS systems and should be considered in any model of OSS development

Stability and sensitivity of Learning Analytics based prediction models

Learning analytics seek to enhance the learning processes through systematic measurements of learning related data and to provide informative feedback to learners and educators. Track data from Learning Management Systems (LMS) constitute a main data source for learning analytics. This empirical contribution provides an application of Buckingham Shum and Deakin Crick’s theoretical framework of dispositional learning analytics: an infrastructure that combines learning dispositions data with data extracted from computer-assisted, formative assessments and LMSs. In two cohorts of a large introductory quantitative methods module, 2049 students were enrolled in a module based on principles of blended learning, combining face-to-face Problem-Based Learning sessions with e-tutorials. We investigated the predictive power of learning dispositions, outcomes of continuous formative assessments and other system generated data in modelling student performance and their potential to generate informative feedback. Using a dynamic, longitudinal perspective, computer-assisted formative assessments seem to be the best predictor for detecting underperforming students and academic performance, while basic LMS data did not substantially predict learning. If timely feedback is crucial, both use-intensity related track data from e-tutorial systems, and learning dispositions, are valuable sources for feedback generation